We propose that quantitative structure-activity relationship (QSAR) predictions should be explicitly represented as predictive (probability) distributions. If both predictions and experimental measurements are treated as probability distributions, the quality of a set of predictive distributions output by a model can be assessed with Kullback-Leibler (KL) divergence: a widely used information theoretic measure of the distance between two probability distributions. We have assessed a range of different machine learning algorithms and error estimation methods for producing predictive distributions with an analysis against three of AstraZeneca's global DMPK datasets. Using the KL-divergence framework, we have identified a few combinations of algorithms that produce accurate and valid compound-specific predictive distributions. These methods use reliability indices to assign predictive distributions to the predictions output by QSAR models so that reliable predictions have tight distributions and vice versa. Finally we show how valid predictive distributions can be used to estimate the probability that a test compound has properties that hit single- or multi- objective target profiles.